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FieldDecompositionSolver (Commons Math 3.2 API)
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org.apache.commons.math3.linear</FONT>
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Interface FieldDecompositionSolver&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt;</H2>
<DL>
<DT><DT><B>Type Parameters:</B><DD><CODE>T</CODE> - the type of the field elements</DL>
<HR>
<DL>
<DT><PRE>public interface <B>FieldDecompositionSolver&lt;T extends <A HREF="../../../../../org/apache/commons/math3/FieldElement.html" title="interface in org.apache.commons.math3">FieldElement</A>&lt;T&gt;&gt;</B></DL>
</PRE>

<P>
Interface handling decomposition algorithms that can solve A &times; X = B.
 <p>Decomposition algorithms decompose an A matrix has a product of several specific
 matrices from which they can solve A &times; X = B in least squares sense: they find X
 such that ||A &times; X - B|| is minimal.</p>
 <p>Some solvers like <A HREF="../../../../../org/apache/commons/math3/linear/FieldLUDecomposition.html" title="class in org.apache.commons.math3.linear"><CODE>FieldLUDecomposition</CODE></A> can only find the solution for
 square matrices and when the solution is an exact linear solution, i.e. when
 ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
 with non-square matrix A and with non-null minimal norm. If an exact linear
 solution exists it is also the minimal norm solution.</p>
<P>

<P>
<DL>
<DT><B>Since:</B></DT>
  <DD>2.0</DD>
<DT><B>Version:</B></DT>
  <DD>$Id: FieldDecompositionSolver.java 1416643 2012-12-03 19:37:14Z tn $</DD>
</DL>
<HR>

<P>

<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html#getInverse()">getInverse</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Get the inverse (or pseudo-inverse) of the decomposed matrix.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;boolean</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html#isNonSingular()">isNonSingular</A></B>()</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Check if the decomposed matrix is non-singular.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html#solve(org.apache.commons.math3.linear.FieldMatrix)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solve the linear equation A &times; X = B for matrices A.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>&nbsp;<A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html#solve(org.apache.commons.math3.linear.FieldVector)">solve</A></B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;&nbsp;b)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solve the linear equation A &times; X = B for matrices A.</TD>
</TR>
</TABLE>
&nbsp;
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<A NAME="solve(org.apache.commons.math3.linear.FieldVector)"><!-- --></A><H3>
solve</H3>
<PRE>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt; <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldVector.html" title="interface in org.apache.commons.math3.linear">FieldVector</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;&nbsp;b)</PRE>
<DL>
<DD>Solve the linear equation A &times; X = B for matrices A.
 <p>The A matrix is implicit, it is provided by the underlying
 decomposition algorithm.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - right-hand side of the equation A &times; X = B
<DT><B>Returns:</B><DD>a vector X that minimizes the two norm of A &times; X - B
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the matrices dimensions do not match.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</A></CODE> - if the decomposed matrix is singular.</DL>
</DD>
</DL>
<HR>

<A NAME="solve(org.apache.commons.math3.linear.FieldMatrix)"><!-- --></A><H3>
solve</H3>
<PRE>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt; <B>solve</B>(<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt;&nbsp;b)</PRE>
<DL>
<DD>Solve the linear equation A &times; X = B for matrices A.
 <p>The A matrix is implicit, it is provided by the underlying
 decomposition algorithm.</p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>b</CODE> - right-hand side of the equation A &times; X = B
<DT><B>Returns:</B><DD>a matrix X that minimizes the two norm of A &times; X - B
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/DimensionMismatchException.html" title="class in org.apache.commons.math3.exception">DimensionMismatchException</A></CODE> - if the matrices dimensions do not match.
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</A></CODE> - if the decomposed matrix is singular.</DL>
</DD>
</DL>
<HR>

<A NAME="isNonSingular()"><!-- --></A><H3>
isNonSingular</H3>
<PRE>
boolean <B>isNonSingular</B>()</PRE>
<DL>
<DD>Check if the decomposed matrix is non-singular.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>true if the decomposed matrix is non-singular</DL>
</DD>
</DL>
<HR>

<A NAME="getInverse()"><!-- --></A><H3>
getInverse</H3>
<PRE>
<A HREF="../../../../../org/apache/commons/math3/linear/FieldMatrix.html" title="interface in org.apache.commons.math3.linear">FieldMatrix</A>&lt;<A HREF="../../../../../org/apache/commons/math3/linear/FieldDecompositionSolver.html" title="type parameter in FieldDecompositionSolver">T</A>&gt; <B>getInverse</B>()</PRE>
<DL>
<DD>Get the inverse (or pseudo-inverse) of the decomposed matrix.
<P>
<DD><DL>

<DT><B>Returns:</B><DD>inverse matrix
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/linear/SingularMatrixException.html" title="class in org.apache.commons.math3.linear">SingularMatrixException</A></CODE> - if the decomposed matrix is singular.</DL>
</DD>
</DL>
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